   Let \((Y_{1},\lambda _{1})\)  and \((Y_{2},\lambda _{2})\)  be any digital images for which \(f : Y_{1} \rightarrow \nolinebreak Y_{2}\)  is digitally continuous. Then \(f\)  is called \((\lambda _{1},\lambda _{2})-\) nullhomotopic [1]} in \(Y_{2}\)  on condition that \(f\)  is \((\lambda _{1},\lambda _{2})-\) homotopic to a constant map in \(Y_{2}\) . Assume now that the digital map \(f : (Y_{1},\lambda _{1}) \longrightarrow (Y_{2},\lambda _{2})\)  is \((\lambda _{1},\lambda _{2})-\) continuous. If there exists a \((\lambda _{2},\lambda _{1})-\) continuous map \(g : (Y_{2},\lambda _{2}) \longrightarrow (Y_{1},\lambda _{1})\)  for which \(g \circ f \simeq _{(\lambda _{1},\lambda _{1})} id_{Y_{1}}\)  and \(f \circ g \simeq _{(\lambda _{2},\lambda _{2})} id_{Y_{2}}\) , then \(f\)  is a \((\lambda _{1},\lambda _{2})-\) homotopy equivalence [2]}. It is said to be that a digital image \((Y,\lambda )\)  is \(\lambda -\) contractible [1]} if \(id_{Y}\)  is \((\lambda ,\lambda )-\) homotopic to a map \(c\)  of digital images for some \(c_{0} \in Y\) , where \(c : Y \longrightarrow Y\)  is defined with \(c(y) = c_{0}\)  for all \(y \in Y\) .
